Mathematics Geometry

mvsd
Math Curriculum 01/12/03

Mathematics - Geometry

Mathematics

The Idaho State Achievement Standards for Mathematics provides skills for kindergarten through twelfth grade.

Connecting: Algebra/Geometry
The learner will be able to apply algebraic skills and ideas to obtain solutions to geometry problems through geometry.

Strand	Bloom's	Scope	Hours	Source
Connecting		Master		District Expectation

Angles: Recognize
The learner will be able to identify angle pairs that are created when two lines are crossed by a transversal.

Strand	Bloom's	Scope	Hours	Source
Angles		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01

Lines/Angles: Identify/Use/Properties
The learner will be able to identify and use inequality properties with the measurements of segments in triangles and angles in triangles.

Strand	Bloom's	Scope	Hours	Source
Lines/Angles/Polygons		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01

Circles: Identify/Define
The learner will be able to recognize and solve problems with circles and their component parts, the lines associated with circles, circle properties, their relationship to polygons, and/or associated angle concepts.

Strand	Bloom's	Scope	Hours	Source
Circles		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Planes/Points/Lines: Apply/Facts
The learner will be able to apply elementary facts about points, lines (perpendicular and parallel) and planes (perpendicular and parallel).

Strand	Bloom's	Scope	Hours	Source
Planes/Points/Lines		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Planes/Points/Lines: Recognize/Define
The learner will be able to recognize, define, or explain and contrast the properties associated with points, lines, planes, segments, rays, and angles.

Strand	Bloom's	Scope	Hours	Source
Planes/Points/Lines		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Properties: Quadrilaterals
The learner will be able to apply properties of quadrilaterals to form and/or test relationships with diagonals, angles, and/or lines of symmetry.

Strand	Bloom's	Scope	Hours	Source
Properties of Figures		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Properties: State/Apply
The learner will be able to state and/or use properties of triangles and/or quadrilaterals of various types.

Strand	Bloom's	Scope	Hours	Source
Properties of Figures		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Right Triangles: Identify
The learner will be able to identify right triangles through the use of elementary congruence postulates and/or theorems.

Strand	Bloom's	Scope	Hours	Source
Right Triangles		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.02 and 348.02; ISAT

Solids: Polyhedrons/Spheres/Parts
The learner will be able to recognize polyhedrons including prisms, pyramids, cubes, tetrahedrons, cylinders, cones, spheres, faces, edges, vertices, bases, and/or lateral edges.

Strand	Bloom's	Scope	Hours	Source
Three-Dimensional Solids		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01; ISAT

Circle Parts: Arc Length
The learner will be able to determine the arc length of a circle.

Strand	Bloom's	Scope	Hours	Source
Circles		Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01

Planes: Recognize
The learner will be able to identify parallel planes.

Strand	Bloom's	Scope	Hours	Source
Planes/Points/Lines		Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01

Congruence: Apply Tools
The learner will be able to apply tools (compass, straightedge, folded paper, mirrors, and/or computers) in the creation of congruent segments, angles, triangles, and/or circles.

Strand	Bloom's	Scope	Hours	Source
Congruence	Application	Master		District Expectation: ISAT

Constructions: Use/Tools
The learner will be able to use tools to create angle bisectors, perpendicular bisectors, a perpendicular line from a point on a line, parallel lines, proportional line segments, tangents, and inscribe and circumscribed polygons.

Strand	Bloom's	Scope	Hours	Source
Constructions	Application	Master		District Expectation; ISAT

Lines/Angles: Identify
The learner will be able to recognize, define, approximate, and/or measure line segments and angles of all kinds.

Strand	Bloom's	Scope	Hours	Source
Lines/Angles/Polygons	Application	Master		District Expectation; ISAT

Parallel Lines: Use/Properties
The learner will be able to use properties that involve parallel lines and/or proportion.

Strand	Bloom's	Scope	Hours	Source
Lines: Parallel/Perpendicular	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.02.b

Similarity: Properties
The learner will be able to identify and/or use properties of similar polygons with the use of ratio and proportion.

Strand	Bloom's	Scope	Hours	Source
Similarity	Comprehension	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01.b; ISAT

Spatial Thinking: Apply
The learner will be able to apply visualization skills to investigate and/or interpret two- and three-dimensional figures using projections, cross sections, and/or locus problems.

Strand	Bloom's	Scope	Hours	Source
Spatial Thinking	Application	Master		District Expectation

Theorems: Apply/State
The learner will be able to state and/or use the triangle sum theorem, exterior angle theorems, and/or polygon angle sum theorems.

Strand	Bloom's	Scope	Hours	Source
Geometric Proofs/Theorems	Knowledge	Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.02.b; ISAT

Three-Dimensional Solids: Areas
The learner will be able to determine the lateral and total areas of right prisms, regular pyramids, right circular cylinders, and cones.

Strand	Bloom's	Scope	Hours	Source
Three-Dimensional Solids	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 349.01; ISAT

Three-Dimensional Solids: Volumes
The learner will be able to determine the volume of solid figures composed of prisms, pyramids, cylinders, cones, or spheres.

Strand	Bloom's	Scope	Hours	Source
Three-Dimensional Solids	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Transformations: Apply
The learner will be able to apply transformations to inspect symmetry, similarity, and/or congruence of geometric figures.

Strand	Bloom's	Scope	Hours	Source
Transformations	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Transformations: Determine
The learner will be able to determine the images of geometric figures under distance-maintaining transformations including line reflections, translations, and/or rotations in space or on a coordinate plane.

Strand	Bloom's	Scope	Hours	Source
Transformations	Comprehension	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a; ISAT

Transformations: Examine/Apply
The learner will be able to inspect and/or use elementary properties of line reflections, translations, rotations, dilations, and/or their compositions to solve Problems.

Strand	Bloom's	Scope	Hours	Source
Transformations	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a; ISAT

Circle Parts: Sector/Area
The learner will be able to compute area of sectors of a circle.

Strand	Bloom's	Scope	Hours	Source
Circles	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a

Congruence: Identify
The learner will be able to recognize congruent figures.

Strand	Bloom's	Scope	Hours	Source
Congruence	Knowledge	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Congruence: Identify
The learner will be able to identify congruence in practical applications.

Strand	Bloom's	Scope	Hours	Source
Congruence	Knowledge	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Congruence: Properties
The learner will be able to apply congruence properties to test conjectures involving triangles.

Strand	Bloom's	Scope	Hours	Source
Congruence	Evaluation	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Geometric Relationships: Problem Solving
The learner will be able to use geometric relationships to solve problems.

Strand	Bloom's	Scope	Hours	Source
Geometric Relationships	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 348.01.a

Inductive/Deductive: Prove/Conjectures
The learner will be able to apply inductive and deductive reasoning to prove conjectures presented in written form.

Strand	Bloom's	Scope	Hours	Source
Reasoning	Evaluation	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 348.02.a

Lines: Identify/Skew
The learner will be able to identify skew lines.

Strand	Bloom's	Scope	Hours	Source
Lines	Knowledge	Master	0.5	District Expectation

Parallel Lines: Identify
The learner will be able to identify parallel lines.

Strand	Bloom's	Scope	Hours	Source
Lines: Parallel/Perpendicular	Knowledge	Master	0.5	District Expectation

Polygons: Classify
The learner will be able to classify polygons as being regular, convex, and/or congruent.

Strand	Bloom's	Scope	Hours	Source
Polygons	Analysis	Master	1.0	District Expectation; ISAT

Problem Solving: Polygons
The learner will be able to use the properties of similar polygons in obtaining problem solutions.

Strand	Bloom's	Scope	Hours	Source
Problem Solving	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 348.02.a; ISAT

Pythagorean Theorem: Apply
The learner will be able to use the Pythagorean theorem and/or the theorem's converse.

Strand	Bloom's	Scope	Hours	Source
Pythagorean Theorem	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.02.c

Pythagorean Theorem: State/Converse
The learner will be able to state the Pythagorean Theorem and its converse.

Strand	Bloom's	Scope	Hours	Source
Pythagorean Theorem	Knowledge	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.02.c

Right Triangles: State/Properties
The learner will be able to state the properties of special right triangles.

Strand	Bloom's	Scope	Hours	Source
Right Triangles	Comprehension	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.02.a

Right Triangles: Use/Properties
The learner will be able to use the properties of special right triangles (30-60-90 and/or 45-45-90).

Strand	Bloom's	Scope	Hours	Source
Right Triangles	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.02.a

Similarity: Figures
The learner will be able to recognize similar figures in practical applications.

Strand	Bloom's	Scope	Hours	Source
Similarity	Knowledge	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Similarity: Triangles
The learner will be able to recognize and solve problems with similar triangles (and other polygons) though the application of their properties.

Strand	Bloom's	Scope	Hours	Source
Similarity	Knowledge	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a; ISAT

Transformations: Dilations
The learner will be able to determine the image of figures under dilations.

Strand	Bloom's	Scope	Hours	Source
Transformations	Application	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.a

Triangles: Classify
The learner will be able to classify triangles as scalene, equilateral or isosceles.

Strand	Bloom's	Scope	Hours	Source
Triangles	Analysis	Master	0.5	District Expectation; ISAT

Triangles: Identify/Congruent
The learner will be able to recognize congruent triangles.

Strand	Bloom's	Scope	Hours	Source
Triangles	Knowledge	Master	0.5	District Expectation; ISAT

Triangles: Sorting
The learner will be able to classify triangles by their angle measures (acute, obtuse, or right).

Strand	Bloom's	Scope	Hours	Source
Triangles	Analysis	Master	0.5	District Expectation; ISAT

Geometry: Postulates
The learner will be able to identify the geometric postulates which form the basis of Euclidean geometry and know what constitutes a postulate.

Strand	Bloom's	Scope	Hours	Source
Geometric Concepts	Knowledge	Master	1.0	ISAT

Angles: Interior/exterior
The learner will be able to identify and calculate the interior and exterior angles of a given figure.

Strand	Bloom's	Scope	Hours	Source
Angles	Application	Master	1.0	ISAT

Circle: Radius/Diameter/Chord
The learner will be able to determine possible values for either radius, diameter, or chords of a circle with given area.

Strand	Bloom's	Scope	Hours	Source
Circles	Application	Master	2.0	ISAT

Reasoning: Apply
The learner will be able to apply formal and/or informal logical reasoning processes.

Strand	Bloom's	Scope	Hours	Source
Reasoning		Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.02

Reasoning: Inductive/Deductive
The learner will be able to apply inductive and/or deductive reasoning skills to form conclusions, recognize conjectures and counterexamples, and to describe the characteristics of a deductive mathematical system.

Strand	Bloom's	Scope	Hours	Source
Reasoning	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.02.a

Reasoning: Recognize
The learner will be able to identify correct deductive reasoning, and create and/or apply if-then, converse, inverse, and/or contrapositive statements.

Strand	Bloom's	Scope	Hours	Source
Reasoning	Comprehension	Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.02.a

Perimeter/Area/Volume: Concepts
The learner will be able to define and/or understand the differences among perimeter, area, and volume and their respective units.

Strand	Bloom's	Scope	Hours	Source
Perimeter/Area/Volume		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.01and 349.01; ISAT

Area: Use/Solve
The learner will be able to obtain solutions to problems using area.

Strand	Bloom's	Scope	Hours	Source
Area		Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.01

Area of a Circle: Calculate
The learner will be able to calculate the area of a circle.

Strand	Bloom's	Scope	Hours	Source
Area of a Circle	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area of a Parallelogram
The learner will be able to calculate the area of a parallelogram.

Strand	Bloom's	Scope	Hours	Source
Area	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area of a Rectangle: Determine
The learner will be able to find the area of a rectangle.

Strand	Bloom's	Scope	Hours	Source
Area of a Rectangle	Application	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area of a Square: Find
The learner will be able to determine the area of a square.

Strand	Bloom's	Scope	Hours	Source
Area of a Square	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area of a Trapezoid: Calculate
The learner will be able to calculate the area of a trapezoid.

Strand	Bloom's	Scope	Hours	Source
Area	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area of a Triangle: Determine
The learner will be able to find the area of a triangle.

Strand	Bloom's	Scope	Hours	Source
Area of a Triangle	Application	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Area: Compare
The learner will be able to make comparisons of the areas of similar polygons.

Strand	Bloom's	Scope	Hours	Source
Area	Analysis	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.b;ISAT

Area: Regular Polygon
The learner will be able to determine the area of a regular polygon.

Strand	Bloom's	Scope	Hours	Source
Area	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Circumference: Determine
The learner will be able to determine the circumference of a circle.

Strand	Bloom's	Scope	Hours	Source
Circumference	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Perimeter: Polygons
The learner will be able to find the perimeter of polygons.

Strand	Bloom's	Scope	Hours	Source
Perimeter	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Perimeter: Use/Solve
The learner will be able to obtain solutions to problems using perimeter.

Strand	Bloom's	Scope	Hours	Source
Perimeter	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 348.01.a; ISAT

Surface Area: Determine/Sphere
The learner will be able to determine the surface area of a sphere.

Strand	Bloom's	Scope	Hours	Source
Surface Area	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 349.01.a; ISAT

Volume: Compare
The learner will be able to make comparisons of the volumes of similar solids.

Strand	Bloom's	Scope	Hours	Source
Volume	Analysis	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.01.b; ISAT

Volume: Use/Solve
The learner will be able to obtain solutions to problems using volume.

Strand	Bloom's	Scope	Hours	Source
Volume	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 348.01.a; ISAT

Formulas: Problem Solving
The learner will be able to solve problems by determining the correct formula to use.

Strand	Bloom's	Scope	Hours	Source
Formulas	Application	Master	2.0	ISAT

Problem Solving: Surface Area/Volume
The learner will be able to solve real world problems using the surface area and volume of three-dimensional solids made up of a combination of basic shapes.

Strand	Bloom's	Scope	Hours	Source
Problem Solving	Application	Master	1.0	District Expectation

Problem Solving: Tools/Techniques
The learner will be able to obtain solutions to problems and practical applications applying suitable techniques and instruments, including calculators and computers.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		ID: State Achievement Standards, 2001, Grades 9-12, 348.01

Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.

Strand	Bloom's	Scope	Hours	Source
Solution	Evaluation	Master	1.5	District Expectation

Coordinate Geometry: Explore
The learner will be able to apply coordinate methods to investigate, conjecture, and/or prove properties of geometric figures through the application of algebra, graphing, and/or suitable technology.

Strand	Bloom's	Scope	Hours	Source
Coordinate Geometry		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.03; ISAT

Coordinate Geometry: Find Point
The learner will be able to determine the coordinates of the point of intersection of two lines through the use of algebra, graphing, and/or suitable technology.

Strand	Bloom's	Scope	Hours	Source
Coordinate Geometry	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.03.a

Coordinate Plane: Graph/Plot
The learner will be able to identify and plot ordered pairs on the coordinate plane.

Strand	Bloom's	Scope	Hours	Source
Coordinate Geometry	Application	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.03.a

Distance: Apply/Formula
The learner will be able to apply the distance formula.

Strand	Bloom's	Scope	Hours	Source
Distance Formula	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 348.01.a

Graphing: Linear Equations
The learner will be able to graph a linear equation.

Strand	Bloom's	Scope	Hours	Source
Graphing	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.03.a; ISAT

Linear Equations: Write
The learner will be able to write the equation of a line.

Strand	Bloom's	Scope	Hours	Source
Linear Equations	Application	Master	0.5	ID: State Achievement Standards, 2001, Grades 9-12, 353.02.a; ISAT

Midpoint: Apply/Formula
The learner will be able to apply the midpoint formula.

Strand	Bloom's	Scope	Hours	Source
Distance Formula	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 351.03.a; ISAT

Slope: Determine/Line
The learner will be able to determine the slope of a line.

Strand	Bloom's	Scope	Hours	Source
Slope	Application	Master	1.0	ID: State Achievement Standards, 2001, Grades 9-12, 350.03.a; ISAT

Coordinate Plane: Ordered Pairs/Area
The learner will be able to plot positions identified by ordered pairs on a coordinate plane and use to determine thee areas of a figure.

Strand	Bloom's	Scope	Hours	Source
Coordinate Geometry	Application	Master	1.0	ISAT

Coordinate Geometry: Apply/Slope
The learner will be able to apply coordinate geometry to find the slopes of lines.

Strand	Bloom's	Scope	Hours	Source
Coordinate Geometry	Application	Master	1.0	ISAT

Right Triangles: Apply
The learner will be able to apply the tangent, sine, and/or cosine ratios for right triangles to obtain solutions to application problems including those involving indirect measurement.

Strand	Bloom's	Scope	Hours	Source
Right Triangles		Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.02

Right Triangles: Identify/Evaluate
The learner will be able to recognize and evaluate tangent, sine, and cosine ratios for an acute angle of a right triangle and apply a table, calculator, or computer to determine the ratio for a given angle or the angle for a given ratio.

Strand	Bloom's	Scope	Hours	Source
Right Triangles	Evaluation	Master		ID: State Achievement Standards, 2001, Grades 9-12, 351.02.a; ISAT

Trig. Ratios: Right Triangle/Solve
The learner will be able to apply right triangle ratios to obtain problem solutions.

Strand	Bloom's	Scope	Hours	Source
Trigonometric Ratios	Application	Master	1.5	ID: State Achievement Standards, 2001, Grades 9-12, 351.02..b; ISAT

Series: Find/Geometric Mean
The learner will be able to find the geometric mean.

Strand	Bloom's	Scope	Hours	Source
Sequences/Series	Application	Master	0.5	District Expectation

Graphing: Predict
The learner will be able to read a graph to predict some future point in time.

Strand	Bloom's	Scope	Hours	Source
Graphing	Knowledge	Master	1.0	ISAT